Orbital Methods and Correlation Errors in Expectation Values

Abstract

The concept of natural spin orbitals (NSO) is one of the most important contributions by Löwdin to quantum chemistry /1/. NSO are defined as eigenfunctions of the one-particle density matrix /1/ γ(1, 1’):

$$ \gamma \left( {1,1'} \right) = N\int {\psi \left( {1,2, \ldots ,N} \right)\psi *\left( {1',2, \ldots ,N} \right)d2 \ldots dN} $$

((1))

In the eigenfunction expansion

$$ \gamma \left( {1,1'} \right) = \sum\limits_i {{v_i}{x_i}\left( 1 \right)x_i^*\left( {1'} \right),} $$

((2))

v _i is interpreted /1/ as the occupation number of the NSO χ_i. A pioneering work on the study of NSO for two-electron systems was carried out by Löwdin and Shull /2–4/. The subsequent theoretical work involved symmetry and convergence properties, whereas the practical work involved calculations on small atoms and molecules. For references we refer to a recent review article by Davidson /5/.